What is factor (a+b)^4-(a-b)^4 ?

The solution to factor (a+b)^4-(a-b)^4 is 8ab(a^2+b^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor (a+b)^4-(a-b)^4

factor

(a + b)^{4} - (a - b)^{4}

8 ab (a^{2} + b^{2})

Solution steps

(a + b)^{4} - (a - b)^{4}

(a + b)^{4} = ((a + b)^{2})^{2}

(a - b)^{4} = ((a - b)^{2})^{2}

= ((a + b)^{2})^{2} - ((a - b)^{2})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

((a + b)^{2})^{2} - ((a - b)^{2})^{2} = ((a + b)^{2} + (a - b)^{2}) ((a + b)^{2} - (a - b)^{2})

= ((a + b)^{2} + (a - b)^{2}) ((a + b)^{2} - (a - b)^{2})

Factor

(a + b)^{2} - (a - b)^{2} : 4 ab

= ((a + b)^{2} + (a - b)^{2}) \cdot 4 ab

Expand

(a + b)^{2} + (a - b)^{2} : 2 a^{2} + 2 b^{2}

= (2 a^{2} + 2 b^{2}) \cdot 4 ab

= 4 ab (2 a^{2} + 2 b^{2})

Factor

2 a^{2} + 2 b^{2} : 2 (a^{2} + b^{2})

= 4 ab \cdot 2 (a^{2} + b^{2})

Multiply the numbers:

4 \cdot 2 = 8

= 8 ab (a^{2} + b^{2})

\frac{2 x + 1}{3 x - 4} \leq - 1

2 x^{2} - 16 x = - 25

\frac{2}{7 - 8 i}

∣ 2 x + 9 ∣ < 9

5 x^{2} - 55 = 90

What is factor (a+b)^4-(a-b)^4 ?
The solution to factor (a+b)^4-(a-b)^4 is 8ab(a^2+b^2)